H2 Optimal Tuning of Passive Isolators and Absorbers

Isolators and absorbers have been studied extensively as a means of passively suppressing vibration in mechanical systems. This paper derives the optimal tuning parameters for these passive suppression schemes with an H2 performance criterion. The H2 norm of a system is briefly reviewed, and its selection as a performance criterion is motivated. The optimal tuning scheme in the case of the absorber is then compared to the classical work of Den Hartog [1] and Snowdon [2]. The comparison shows little improvement in the H2 cost over the classical scheme, which suggests that the approximately optimal H∞ analysis of the absorber respects the optimal H2 cost. However, the reverse is generally not true, as in the case with increasing absorber masses.